The use of computer graphics for solving problems in singularity theory
Visualization and mathematics
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Review
Shock Graphs and Shape Matching
International Journal of Computer Vision
Boundary Smoothing via Symmetry Transforms
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Hierarchical Decomposition and Axial Shape Description
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock-Based Indexing into Large Shape Databases
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
A shock grammar for recognition
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
On the Intrinsic Reconstruction of Shape from Its Symmetries
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Mathematica Book
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
On Evolute Cusps and Skeleton Bifurcations
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Affine Invariant Medial Axis and Skew Symmetry
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Deep Structure, Singularities, and Computer Vision: First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers (Lecture Notes in Computer Science)
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Computing 3d symmetry sets; a case study
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Deriving the Medial Axis with geometrical arguments for planar shapes
Pattern Recognition Letters
Contour Grouping Based on Contour-Skeleton Duality
International Journal of Computer Vision
Computationally efficient matching of microRNA shapes using mutual symmetry
SIP '07 Proceedings of the Ninth IASTED International Conference on Signal and Image Processing
On the Local Form and Transitions of Pre-symmetry Sets
Journal of Mathematical Imaging and Vision
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Among the many attempts made to represent families of 2D shapes in a simpler way, the Medial Axis $$\mathcal{MA}$$ takes a prominent place. Its graphical representation is intuitively appealing and can be computed efficiently. Small perturbations of the shape can have large impact on the $$\mathcal{MA}$$ and are regarded as instabilities, although these changes are mathematically known from the investigations on a super set, the Symmetry Set $$\mathcal{SS}$$. This set has mainly been in a mathematical research stage, partially due to computational aspects, and partially due to its unattractive representation in the plane.In this paper novel methods are introduced to overcome both aspects. As a result, it is possible to represent the $$\mathcal{SS}$$ as a string is presented. The advantage of such a structure is that it allows fast and simple query algorithms for comparisons.Second, alternative ways to visualize the $$\mathcal{SS}$$ are presented. They use the distances from the shape to the set as extra dimension as well as the so-called pre-Symmetry Set and anti-Symmetry Set. Information revealed by these representations can be used to calculate the linear string representation structure.Example shapes from a data base are shown and their data structures derived.